@@richarde.borcherds7998 Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. Integration is dual to differentiation. Divergence (entropy) is dual to convergence (syntropy). The word entropy means "a tendency to diverge" or differentiate into new states -- reductionism. The word syntropy means "a tendency to converge" or integrate into a whole -- holism. "Entropy is a measure of randomness" -- Roger Penrose. Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics! "Always two there are" -- Yoda. The unit circle in optimized control theory = the margin of stability (photons, light). Inside is dual to outside. Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes. Concepts are dual to percepts -- the mind duality of Immanuel Kant. "Perpendicularity in hyperbolic geometry is measure in terms of duality" -- Professor Norman Wildberger -- universal hyperbolic geometry.
Thank you for the beautiful lectures! Please keep sharing them.
Great lecture series; I've studied many of these things in the past but this is so illuminating.
You are awesome sir!
Amazing video, in those 20 minutes I learned more than in my undergraduate semester course.
But don't we need f to be continuous in Morera's theorem?
Yes, I should have said f is continuous.
@@richarde.borcherds7998 Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
Integration is dual to differentiation.
Divergence (entropy) is dual to convergence (syntropy).
The word entropy means "a tendency to diverge" or differentiate into new states -- reductionism.
The word syntropy means "a tendency to converge" or integrate into a whole -- holism.
"Entropy is a measure of randomness" -- Roger Penrose.
Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics!
"Always two there are" -- Yoda.
The unit circle in optimized control theory = the margin of stability (photons, light).
Inside is dual to outside.
Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
"Perpendicularity in hyperbolic geometry is measure in terms of duality" -- Professor Norman Wildberger -- universal hyperbolic geometry.
At 17:00, wouldn't the condition be |z| > R instead of |z| < R?
For the first application...anyone knows why f is hol. on C but not necessarily inside C? 4:56
It's just an assumption i.e. "let's assume f is on hol on C, what can we then say about f inside C using this theorem we just proved?"
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⭕ everywhere love 💕
I didn't get it on the proof cauchy's integral formula RUclips.lecturer kindly repeat the concept in a different manner